When relative humidity is high – meaning that the air is holding a lot of the moisture that it can hold at a given temperature – it becomes more difficult to cool yourself down. We cool ourselves down by sweating: we sweat, the sweat evaporates into the air, and (in ELI5 terms) takes some energy with it, cooling you slightly.
When the air is already holding a lot of moisture, your sweat is less likely to evaporate because it has nowhere to go – the air is full. That means you get much less of this cooling effect.
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